Mathematics is an entirely separate category of science from physics, biology, chemistry etc. Where Physics you study the universe and it's contents, biology you study living organisms, chemistry is interactions of nanoscopic particles. But math is just math. You can't really see it, so it's more like a tool for other sciences, right?

Maybe..

The question is, did human beings discover or invent mathematics?
On one side the discovery of math implies that it is a universal property of everything, everything uses math, it implies that there is more math to be discovered, named and synced with our current understanding of math. It may also go to lengths even to say that there is math waiting for us to discover that resembles nothing like what we have and that we don't understand even after its discovery.

The other side however, invention, implies that humans needed at multiple stages in our evolution ways of understanding things and from that ways to understand other things from information about things we already know. It also implies more or less math does not exist in reality but only in our minds, as a tool to figure out how to smash open a coconut and when we decide that we want to know how the tool works, we invent.. More math..

So I'm very interested about what you intellectuals have to say here about if it's just humans using math or rocks, and platypuses, and supernovae.
Everybody keep it clean and you must realise that there is no real solid answer to this question so respect everyone's opinion even when it doesn't coincide with yours, thank you

Mathematics is a language we use to describe values and trends we observe in the world that we otherwise couldn't explain. Why is it that if I hold up four fingers it's four fingers not five? It is because we have assigned the word "four" to explain that value.

The patterns, values and trends that mathematics describes have existed since the world began (possibly earlier) and always will but the symbols and equations we use to explain these things - the language we call maths - are of humanities creation.

We invented a way of communicating mathematical concepts to each other but the underlying mathematical / physical principles that govern this world have always existed. So humans over time discovered these phenomena and then created a universal way of expressing these things to each other.

But to give a more definitive answer, humans created Mathematics as a language of logic.

The patterns, values and trends that mathematics describes have existed since the world began (possibly earlier) and always will but the symbols and equations we use to explain these things - the language we call maths - are of humanities creation.

It's interesting that your understanding of math is of a language rather than the values they describe.
I imagine that in the absence of humanity and therefore the language of math, the universe still functions and principles therefor exist. So I feel technically we discovered it much the same as we discover distant objects and the remains of strange creatures from millions of years ago and then name them accordingly.

I think it all comes down to how you understand what mathematics really is. For me it's what's behind the language.

@Plumpy - Well here's one way of putting it; rocks have existed for a very long time, whilst the English language is still a baby in the context of the universe. As far as humans in the dark ages knew those rocks had always been there but it was the first English speakers that came up with the word "rock" to describe this object that had always been around. It is the same for mathematics, we came up with the symbols and equations we are familiar with to describe things that have always existed.

In the same way that humans began using the word "rock" to refer to the object we use numbers and symbols to explain trends, values and patterns that exist around us. This doesn't mean that the English language and rocks are the same thing, why should the language of mathematics be any different?

@Black Ice - Math doesn't govern the universe. We use math to describe/explain the scientific principals that govern the Earth. We didn't invent these principals, they have been around as long as our universe, we discovered them. But the language we use to explain these things (maths) is of human invention (see my above explanation).

So you do understand the general direction in which I'm coming from gimmepie. But I'm thinking slightly deeper not that in that a rock is what makes up the word "rock" but that the language of which the word was made for had existed before the word was made and even before the word "language" was created to describe it.

Language is a poor example because of its obvious invention and use only by humans, but can be adopted here if you take mathematics as hypothetically the "language" of the universe.

I understand that, what I'm saying is that you are calling the principals mathematics describes the same thing as mathematics which is untrue.

Gravity, electromagnetisms, values, trends, patterns - these things have been around as long as the universe. But the mathematics we use to explain these things is a language we have created no different to English or Chinese. Mathematics, as you so put it, is "an obvious invention and used only by humans".

@Black Ice - Math doesn't govern the universe. We use math to describe/explain the scientific principals that govern the Earth. We didn't invent these principals, they have been around as long as our universe, we discovered them. But the language we use to explain these things (maths) is of human invention (see my above explanation).

thats what i meant. if you bothered to read my post i said basically the same thing. and why are you saying "to the earth" when you know it explains the entire universe. don't simplify and don't be a pedant.

in any case this thread is the ****ing stupidest thing because math is obviously our language while the principles they describe can't be changed. the argument is basically asking if math is both a language and a principle.

Might as well just say this: I agree with the above. Maths (Get it right, Yanks :P ) is our way of explaining the universe, like the laws of Physics etc. Some of it may be perfectly correct, other parts may need correcting (like the mistaken belief that the Earth was the centre of the universe).

It depends on your point of view. At it's heart, this is actually a truly philosophical discussion. It's usually simply put as the philosophy of mathematics. I get to use my philosophy minor!

The concepts that math describes have always existed, but math itself, its formulas and equations, are all man made.

My reasoning: I lean more toward contructivism, more associated with language and learning.

Humans, as a result of language, are visual people. How do we teach children new words? We hold up the item and tell them the word associated with it. How do we teach children to read? We use flashcards with the item pictured on one side and the word written on the other. And it's not purely visual. We associate letters to coincide with sound, and random letter pairings into words, and those words become the item. Did you know that most people don't even had to read words in order to understand them? Who hasn't seen that paragraph explaining this. That our brains only care about the first and last letter of a word. Why? Because we view the word as a whole. We are a visual society, further confirmation.

What it all comes down to is language and answering the question of what is math? Math, at its heart, is a language. So what is a language? A language, like math, has its own rules, etc, but that's not what I am focusing on.

Language is how man associates with the world around him. Try to describe something without words, like an apple. You can't, it's impossible. Language has become one with how we associate with reality, so naturally we try to understand reality within the confines of something we can understand, math... language.

Math is just another language, another way for humanity to describe reality. Some would even call it the perfect language, since say, there is no way to mistake 6 for 4.

in any case this thread is the ****ing stupidest thing because math is obviously our language while the principles they describe can't be changed. the argument is basically asking if math is both a language and a principle.

philosophy isn't stupid because you don't understand it. This is a chicken or the egg debate essentially.

@Amore: I'm Australian, this is the only time I've ever agreed with American Grammar. Mathematics is not plural so to shorten it into something resembling plural is misleading, hence math. But feel free to call it as you like that's not the point of this thread.

@Gimmepie: Now prove to me a square isn't a cube from face only view without manipulating it, you can't prove it and you can't disprove it so we both have different views of this super-positioned square and neither of us are wrong.

Okay I misspoke, i meant I was referencing English language.

@PhantomX0990: But wouldn't you suppose that being the "perfect language" we can comfortably acknowledge it as more than it describes without context.
In actual fact a picture can describe something quite well, I have a picture of an apple, you note its size, colour, shape and even its flavour and texture from past experience.
And if we describe math without words we don't get any other form of studied science, we get the tools to study all of those sciences.
Besides we define Physics as a study but I would still call gravity physics far before Newton and Einstein existed.

@PhantomX0990: But wouldn't you suppose that being the "perfect language" we can comfortably acknowledge it as more than it describes without context.
In actual fact a picture can describe something quite well, I have a picture of an apple, you note its size, colour, shape and even its flavour and texture from past experience.
And if we describe math without words we don't get any other form of studied science, we get the tools to study all of those sciences.
Besides we define Physics as a study but I would still call gravity physics far before Newton and Einstein existed.

A picture could give the idea of a thing. But that's not essentially the description. You could draw a picture of an apple, color it in red. I then could point at the red color, and ask, what is that? You'd say that's the apple. I'd say, no, what's that color? You'd say, that's red. I would the ask, what is red?

Exactly. Language is, in essence, our link to reality. Take it away and we have our thoughts and ideas. Those tools that we would be left with are the same as language. For language is not just spoken, but thought. It is our entire thought process. You cannot think of something without thinking of its associated word.

I'd call physics a study, yes I suppose... but isn't gravity a physical truth? It still existed before we had a word for it... now we do. Now that's all it is... a word, an idea. We labeled a fact. Langauge is powerful ****. Kinda blows the mind.

For once I find myself agreeing - at least in part with Black Ice. Calling it a Chicken and the Egg debate is a fairly poor comparison, because it is fairly obvious that the principals existed long before the language did.

@Black Ice - You're not doing much to contribute to the conversation by coming in here and knocking the thread and those contributing though. It doesn't matter if you think this is a stupid debate (which makes you participating in it rather interesting - no offence intended) all that matters is the debate itself.

@Plumpy - Okay you got me on your latest Square vs Cube, I can't out do you on that one. But I still must disagree with your assessment as this of a situation with no right or wrong and only different views. Either maths is a language we invented, a principal we discovered, or two sides of the same coin. There's not really any grey area - one of those categories is correct and only one. But I appreciate how you are trying to look at this.

As for the debate itself - Language and images are two related but separate entities that are both a part of literacy. That's the way I see that little side-step.

More on topic - Let me ask you this. If you discovered a brand knew principal today, you would probably name it correct? Quite probably after yourself. But this principal most likely existed long before you would have named it, you are simply attaching this title to the principal so you are able to refer to it. Before naming it you may have simply used a question mark to denote it in your research notes, but you have still essentially used a language to brand it.

Since it is a mathematical principal you have hypothetically discovered you undoubtedly have a formula that represents it, but again the principal itself existed long before you used a formula to denote it.

Did you discover the principal in this scenario? Yes
But you didn't discover the language you use to describe it, whether that is it's name in English or the Formula you have used to represent it. The language you are using is a human invention - we created it to communicate at a higher level, to describe objects and their components, and have refined it over time.

You will probably argue that you may have discovered the formula for this principal. But I have a counter-argument for that: You discovered the workings of the formula, a principal, the formula itself you invented. Say you decided to us a/q*x = t as your formula. Value one divided by value two then multiplied by value three equals value four. Where

Value 1 = a
Value 2 = q
Value 3 = x
Value 4 = t

In this scenario, you have determined what each of those values is denoted by. You could have just as easily used the letter b, z, r and w to represent the values in your formula - and if one of those values corresponds to an already discovered principal that just means someone else went through the same process for that value earlier on where they discovered the value and then used language to represent it.

you cant argue with the fact that people at first noticed maths in nature , from the making of the pyramids to the working of a simple wheel , humans observed this trend and then adapted and advanced with this trend .

various fields for example calculus, both differentiation and integration arose from graphs , although very crudely but then it was formed into what it is now .
basically everything that is there today in mathematics started with someone noticing it or in other words discovering it if you may .

maths like many other things are very hard to perfect , even today there are many unsolvable problems in math and gradually news are arising that there are people who are able to now solve 100+ year old unsolved questions implying that how much ever techniques and methods we use there will still be quite a bit more in the future.

i agree with you saying we invent mathematics on the go, its only when we hit a obstacle for which there isn't already a method to overcome it that we sit down and think hard and come up with a way . all forms of science are deeply inter related with maths , physics,biology and chemistry(the major one's ) in fact some of them are like how human bodies are made of a vast majority of water.

@Plumpy - Okay you got me on your latest Square vs Cube, I can't out do you on that one. But I still must disagree with your assessment as this of a situation with no right or wrong and only different views. Either maths is a language we invented, a principal we discovered, or two sides of the same coin. There's not really any grey area - one of those categories is correct and only one. But I appreciate how you are trying to look at this.

More on topic - Let me ask you this. If you discovered a brand knew principal today, you would probably name it correct? Quite probably after yourself. But this principal most likely existed long before you would have named it, you are simply attaching this title to the principal so you are able to refer to it. Before naming it you may have simply used a question mark to denote it in your research notes, but you have still essentially used a language to brand it.

Did you discover the principal in this scenario? Yes
But you didn't discover the language you use to describe it, whether that is it's name in English or the Formula you have used to represent it. The language you are using is a human invention - we created it to communicate at a higher level, to describe objects and their components, and have refined it over time.

In this scenario, you have determined what each of those values is denoted by. You could have just as easily used the letter b, z, r and w to represent the values in your formula - and if one of those values corresponds to an already discovered principal that just means someone else went through the same process for that value earlier on where they discovered the value and then used language to represent it.

The square cube thing is my go to two-part rebuttal for similar applicable situations, I've had practice with that one hahah.

Alright yeah you got me there, there isn't much I can say without repeating myself or just alienating mathematics from language.

Whilst I am on the same side as you in this debate Crow, I have to disagree with your arguments. Logic is far from a human concept. We are possibly the most illogical being to exist or that ever will exist, even more so because we can recognise logical actions and decisions and then voluntarily take a different one. Further more, who is to say that aliens on some far off planet aren't highly logical beings? We didn't create logic, it (like the principals we describe with mathematics) is just something we can identify and imitate or explain.

That is interesting you bring it up though Crow, logic is a key defining aspect of math and I think it should be considered.

I agree that logic was created, someone/thing must have specifically gone out of their way to deem something logical. But what is logical? Newtonian physics is logical, quantum physics is most definitely not. But who's to say that if quantum physics was discovered first it would remain illogical.
Maintaining my stance in the original debate, I think logic is independent of whether or not math was created, because it itself had to be defined before we could claim anything was logical or not.

I’m pretty new to debate but I now finally had the courage to try and say what I can because I know that PC is one of the friendliest communities around I have ever seen (right? :D). This is a complicated subject and I tried my best to express my opinion about this topic (Gosh this took so long for me to write):

I think whatever in math was right has been discovered and whatever is incorrect in math has been invented because our world functions through those concepts that work. We count and the theory of counting is right in its own sense. Our most common style of counting, which is the foundation of maths everywhere (1,2,3,4), has been invented. There are other styles of counting such as by Base 13, when numbers are counted as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, and C. It's like counting with 13 fingers instead of 10. And we may switch the numbers up into characters or random symbols and they can still represent a correct counting system. Counting is true, that's a known fact. If that wasn't true math, there would be a whole set of assumptions because there is nothing for them to stand on and develop into ideas that represent truth. (It would be so confusing without any numbers because we need them to explain lots of other phenomena)

If counting is true, shouldn't the mathematical operations be true (e.g. addition/multiplication)?
We can immediately apply it into our lives, but we can shift the symbols anyhow we want it to be. x can be c, and + may be switched around with -. But it is still true if the concept underlying the symbols are true.

We can attempt to explain the other theories of math by the use of the established theories proven to be facts (e.g. counting and arithmetic operations (+,-,x). Physics is another case. Just because the math is right doesn't make it true. Physics is the science of observation backed up by the absolute truth of mathematics. We try to explain physics phenomena rationally by math. The phenomena are right, but how did they happen? That is the question we want to answer by observation followed by math. But just because the thought is rational and the math is right doesn't make it true. We might have observed and applied math at the wrong place.

For ex.: Gravity is true. It is a known fact. Humanity saw things falling to the ground and attempted to explain it. But gravity is a really complicated and the theories and hypothesis made to explain it may be either true or false due to wrong scope (wrong scope = focusing on assumptions/ wrong area // And assuming that the math concepts behind it is perfect), but it doesn't change the fact that gravity is true and a fact of life.

I heard someone mentioned a cube and square. We can find the area and volume of a cube/square by various formulas but the style of those may be different. But it works, so shouldn’t it be true because volume and areas exist in every kind of 2-D and 3-D shapes imaginable?

Humanity has discovered the right areas of mathematics and invented the false theories of mathematics because our world cannot function through wrong theories about math. Math is the order of life. Our world functions cannot exist without math.

I think whatever in math was right has been discovered and whatever is incorrect in math has been invented...

I heard someone mentioned a cube and square. We can find the area and volume of a cube/square by various formulas but the style of those may be different. But it works, so shouldn’t it be true because volume and areas exist in every kind of 2-D and 3-D shapes imaginable?

This entire post.
I've quoted here because I want to point out we were discussing assuming as if it was all correct, but I like your ideas.

The cube/square scenario was describing perspective, so if you look at a cube face on it looks like a square right? But if you have had and can not have any other view of the cube other than face on you would assume it was simply a square and had no evidence to prove otherwise .

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